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/. theor. Biol. (1999) 198, 239-257 

Article No. jtbi. 1999.09 13, available online at on IIEJ^L 


Cytological, Genetic and Evolutionary Functions of Chiasmata Based on 

Chiasma Graph Analysis 

Hirotami T. Imai*1\ Masayasu Y. WadaJ, Hirohisa Hirai§, 
Yoichi Matsuda^I and Kimiyuki Tsuchiya|| 

^National Institute of Genetics, Mishima, Shizuoka-ken 411-8540, Japan, 
%Amagi Wild Boor Park, Amagiyugashima, Shizuoka-ken 410-3206, Japan, 
^Primate Research Institute, Kyoto University, Inuyama, Aichi-ken 484-8506, Japan, 
^School of Bioagricultural Sciences, Nagoya University, Nagoya, Aichi-ken 464-8601, 
Japan and \\ Experimental Animal Center, Miyazaki Medical College, Kiyotake-cho, 

Miyazaki-ken 889-1692, Japan 

{Received on 10 June 1998, Accepted in revised form on 26 January 1999) 

The nature of the chiasma as a cytological parameter for analysing crossing-over was 
reexamined quantitatively by an improved chiasma graph method. It was reconfirmed in Mus 
platythrix (n = 13) that interstitial chiasmata at diakinesis are distributed randomly and 
almost uniformly along bivalents except for the centromere and telomere regions. The size 
of these chiasma blank regions was consistently 0.8% of the total length of haploid autosomes 
in all chromosomes. There was a minimum value of chiasma interference distance between 
two adjacent chiasmata, which was constantly 1.8% in all chromosomes. The chiasma 
frequency at diakinesis was 20.1 ± 2.0 by the conventional method including terminal 
chiasmata. However, the primed in situ labeling technique revealed that terminal chiasmata 
were mostly telomere-telomere associations. From these data and also from recent molecular 
data we concluded that the terminal chiasma is cytologically functional for ensuring the 
normal disjunction of bivalents at anaphase I, but genetically non-functional for shuffling 
genes. The chiasma frequency excluding terminal chiasmata was 14.6 ± 1.8. Reexamination 
of the chiasma frequency of 106 animal species revealed that the chiasma frequency increased 
linearly in proportion to the haploid chromosome number in spite of remarkable difference 
in their genome size. The increase in chiasma frequency would be evolution-adaptive, because 
gene shuffling is expected to be accelerated in species with high chromosome numbers. 

© 1999 Academic Press 


Modern aspects of crossing-over have been 
framed by the finding of the synaptonemal 

f Author to whom correspondence should be addressed. 

complex (SC) (Moses, 1968) and the recombina- 
tion nodule (RN) (Carpenter, 1975). It has been 
accepted that the SC is a prerequisite for synapsis 
of homologous chromosomes and for initiating 
meiotic recombination (Rasmussen & Holm, 
1980; von Wettstain et al, 1984). 

0022-5193/99/010239 + 19 $30.00/0 

© 1999 Academic Press 



This well-known view has been challenged 
recently by the genetic and molecular evidence 
from yeast suggesting that both homology search 
and meiotic recombination can occur without SC 
formation (Kohli & Bahler, 1994; Loidl et al, 
1994; Sym & Roeder, 1994). 

The latest paradigms related to the meiotic 
processes are as follows: (1) there are two types 
of recombination nodules (early- and late-RNs): 
the early-RNs are involved in gene conversion 
and homology search initiating synapsis, and the 
late-RNs are involved in genetic recombination 
leading to chiasma formation; (2) the major 
functions of SC are to stabilize recombination 
intermediates (heteroduplexes), to transform 
them into functional chiasmata, and to control 
the chiasma distribution known as chiasma 
interference (for reviews see Carpenter, 1987; 
Ashley, 1994; Loidl, 1994; Moens, 1994; Egel, 
1995; Scherthan, 1997). These new paradigms 
suggest a strong causal relation between chiasma 
and crossing-over as the cytological expression 
of genetic recombination. 

Since the first finding of chiasma by Janssens 
(1909, 1924), the chiasma distribution on 
bivalents and the chiasma frequency per cell have 
been considered useful cytological parameters 
for analysing crossing-over, and hundreds of 
reports on chiasma analysis have been published 
(for review see John, 1990). After careful 
consideration, we found unexpected evidence 
that most reports might have been misled by the 
chiasma terminalization hypothesis (Darlington, 
1929, 1932) and by the inappropriate statistical 
methods used for describing chiasmata. 

If interstitial chiasmata move to chromosome 
termini during meiotic prophase I, cytological 
information of crossing-over which is recorded 
on bivalents as the locality and frequency of 
chiasmata will be biased or lost. Although the 
concept of chiasma terminalization has been 
negated by the confidential evidence of 
differential chromatid staining after BrdU 
incorporation (Tease, 1978; Kanda & Kato, 
1980; Jones & Tease, 1984), it has affected the 
calculation of chiasma frequency for a long time, 
and the bias is reflected still in the term "terminal 

Alternative interpretations of the nature of 
terminal chiasma have been proposed: for 

example, terminal chiasma in the literal meaning 
of the word, a kind of interstitial chiasma 
occurring in pseudoautosomal or subterminal 
regions, achiasmatic terminal association and so 
on (for review see Jones, 1987). These possibili- 
ties will be discussed critically in later sections 
based on the cytological, genetic and evolution- 
ary functions of the chiasmata. 

The other serious problem is concerned with 
the statistic representation of chiasma measure- 
ment. The location of each chiasma was 
measured down to two decimal places in most 
cases, but the frequency distribution of the 
chiasmata has been scored at every 2.5 or 5 or 
10% interval in each arm length of the examined 
chromosomes (e.g. Henderson, 1963; Southern, 
1967; Shaw & Knowles, 1976; Saadallah & 
Hulten, 1983; Lawrie et al., 1995) or more 
roughly (Proximal, /nterstitial, Z)istal, and 
Terminal) (John & King, 1985a). As the absolute 
length of the unit interval alters with chromo- 
some size, it is methodologically difficult to 
compare the chiasma distributions quantitatively 
(using the same scale) between morphologically 
different chromosomes of heterogeneous kary- 
otypes in different organisms. 

Recently, we proposed a new method (chiasma 
graph method) for the quantitative analysis of 
chiasmata (Wada & Imai, 1995; Hirai et al., 
1996a). In the chiasma graph, the location of the 
chiasmata can be described quantitatively by two 
parameters, which are the size of the chromo- 
some arms and the distance from the centromere 
in each arm, both of which are given as a 
percentage of the total length of autosomal 
bivalents. This method can be applied generally 
to chiasmate eukaryotic karyotypes having 
localized centromeres, and will provide new 
insights into terminal chiasma, chiasma distri- 
bution, chiasma frequency, and chiasma inter- 

In the present paper, we first outline the 
chiasma graph method using a mammalian 
species Mus platythrix with n = 13, and reexam- 
ine the chiasma frequency of various animals 
with different chromosome numbers (n = 2-46), 
then finally discuss a possible role of the chiasma 
in eukaryotic chromosome evolution with 
reference to the minimum interaction theory 
(Imai et al, 1986). 



Materials and Methods 


Chromosomes were prepared from the testes 
of mature Mus plathythrix having n = 13 
(Muridae, Rodentia, Mammalia) using the 
air-drying method of Imai et al. (1981). For 
chiasma analysis, chromosome preparations 
were stained by conventional Giemsa staining, 
and well-spread meiotic figures at diakinesis were 
used. Centromeres were identified using the 
modified silver staining method of Howell & 
Black (1980) (for details see Wada & Imai, 1991). 


To obtain molecular level information about 
the so-called terminal chiasma, we applied the 
PRINS technique to telomeres (TTAGGG)„. 
The PRINS technique has been developed and 
established recently to directly localize sequences 
using oligonucleotide primers (e.g. Koch et al., 
1989; Gosden et al., 1991; Gosden & Hanratty, 
1993). This method is more rapid, simple and 
sensitive than the conventional in situ hybridiz- 
ation with cloned probes (FISH). 

The PRINS reaction was conducted in 
accordance with the manufacturer's protocol for 
the PRINS reaction set (Boeheringer Mannheim: 
1695932). The 30 ul aliqot of reaction mixture 
contained lOOpmol of oligonucleotide primer 
(CCCTAA) 7 (Therkelsen et al., 1995), 3 ul of 
PRINS labeling mix (1 1 uM each dATP, dCTP, 
and dGTP; 1.1 uM digoxigenin-1 1-dUTP), 3 ul 
of 10X PRINS reaction buffer, and 3 units of 
Taq DNA polymerase. 

The mixture solution was dropped onto a 
slide, which was covered with a clean 
22 x 40 mm 2 cover slip and sealed with rubber 
cement (Elmer). The slide was left in a 
refrigerator until the rubber cement dried, then 
was transferred to the plate of the OmniGene 
In-situ Block (Hybaid, HB-TR3-CMFB). 

The PRINS program was as follows (see also 
the Instruction Manual of OmniGene): (1) the 
simulated slide control was selected, which 
adjusts the surface of the slide to a selected 
temperature (thus, the thickness of the slide must 
be less than 1 mm); (2) the slide was kept at 93°C 
for 5 min to denature the chromosomal DNA, 
then (3) 61°C for 30 min to anneal and extend. 

After the PCR reaction, the cover slip was 
removed and the slide was transferred to stop 
buffer (50 mM NaCl, 50 mM EDTA) at 60°C for 
3 min. 

Signal detection was conducted by the 
technique of Hirai & Lo Verde (1995). The slide 
was washed three times in BN buffer (0.1 M 
sodium bicarbonate and 0.1% Nonidet P-40) for 
3 min each. After blocking with 50 ul of milk BN 
buffer (5% non-fat milk BN buffer) for 10 min 
at 37°C, the positive region was stained with 
50 ul of anti-digoxigenin-fluorescein conjugate 
(Boehringer Mannheim) (800 ng in 5% non-fat 
milk BN buffer) at 37°C for 30 min in the dark. 

After the staining reaction was stopped, the 
slide was washed twice with BN buffer for 10 min 
each time on a shaker at room temperature. 
Chromosomes were counterstained with 20 ul of 
anti-fade solution containing propidium iodide 
(PI, 30 ng ml" 1 ). 

The slide was covered with a 24 x 40 mm 2 
cover slip, then signal observations were made 
after the removal of surplus solution. Data were 
assessed on an Axiophoto epifluorescence micro- 
scope and recorded as images in a computer by 
a Photometrix CCD camera system. 


For quantitative analysis of chiasmata, we use 
the chiasma graph method (Wada & Imai, 1995) 
with modifications. The major terminologies for 
describing chiasmata in the chiasma graph 
method are represented schematically in Fig. 1. 
The brief outline follows. 

We use bivalents at diakinesis, because 
chiasma analysis tends to be biased by artificial 
pseudochiasmata due to chromosome twisting at 
diplotene and hyper-contraction of bivalents at 
metaphase I (for details see Wada & Imai, 1995). 
Images of an acrocentric and a submetacentric 
chromosome at mitotic metaphase and diakine- 
sis ( = bivalents) are shown in Fig. 1(a) and 1(b). 

Chiasma and chiasmata are conventionally 
abbreviated to "Xa" and "Xta" (e.g. Darlington, 
1932; Henderson, 1963; Southern, 1967; John, 
1990). We use "X" for both, because "X" in 
italic form (X) represents the chiasma distance 
and "Xt" represents terminal chiasma(ta) in the 
present paper. 



The locations of chiasmata (X) on bivalents 
(chiasma distance) are defined by the distance 
from the centromere on the short (S) or long (L) 
arms [Fig. 1(c)]. The short or long arms are used 
simply as arms (SL) in the chiasma graph 
[Fig. 1(d)]. 

The length of the arms (abbreviated SL) and 
the chiasma distance (X) are described quantitat- 
ively as a percentage of the total length of the 
autosomal bivalents at diakinesis, which is 
proportional to the total length of the synap- 
tonemal complex (SC) at pachytene. The sex 
chromosomes were excluded from the total 
bivalent length, because the X and Y chromo- 
somes are usually heteromorphic and their 
contraction during meiosis I is not synchronized 
with that of the autosomes. 

Chiasma(ta) (X) are classified into three basic 
categories: centromeric chiasma (Xc or Xc 
chiasma), /nterstitial chiasma (Xi or Xi chiasma) 
and /erminal chiasma (Xt or Xt chiasma). Their 

locations on arms are given by the distance from 
the centromere (i.e. chiasma distance), respect- 
ively, as Xc = 0, < Xi < SL and Xt = SL [Fig. 
1(d)]. As the chiasma formation is inhibited at 
the centromere, the Xc chiasma is a theoretically 
ideal chiasma. 

We use a new concept of "compound 
chiasma" for a set of chiasmata observed on the 
same arm. There are four types: mXi, mXi.IXt, 
lXt and OX chiasma. For example, mXi chiasma 
means m numbers of interstitial chiasmata (Xi) 
on the same arm (m ^ 1). In the mXi chiasma, 
each interstitial chiasma is named from the 
proximal to the distal mXi h mXi 2 , . . ., mXij, . . ., 
mXi m , where the chiasma distance is mXi u mXi 2 , 
. . ., mXij, . . ., mXi,,, [1 <y < m, Fig. 1(d)]. The 
arms with mXi, wXi.IXt, lXt and OX chiasmata 
are termed mXi, mXi.IXt, lXt and OX arms at 
need. We use "mXi fraction" for the mXi 
chiasmata included in mXi or mXi.IXt chias- 



(a) bd - — t — 







, lXt 

(b) bd — t- 








Fig. 1 . Diagrammatic representation of terminologies and basic concepts used in the improved chiasma graph method, 
(a, b) An acrocentric or submetacentric chromosome at mitotic metaphase (left) and meiotic pro-metaphase I (right), and 
chiasmata (lXt, lXi, 2Xi, and 2Xi 2 ) on short or long arms (SL) in the latter. Black parts with constriction are the centrome 

(c) and pericentromeric heterochromatin. White or shadowed columns represent the euchromatic arms. Open circles are 
telomeres (t); (c) four arms of the chromosomes in (a) and (b), where their centromeres are arranged properly to the left; 

(d) a general scheme of locations of chiasmata (Xc, Xi, Xt) and chiasma interference distance (Ic, li, It) on arms (SL). SL 
the size of arms. 



Three categories of chiasma interference 
distance (Ic, Ii and It) are used here [Fig. 1(d)]. 
The terms Ic and // correspond to the differential 
distance "d" and the interference distance "/'" of 
Mather (1937). The Ii value means the chiasma 
distance between two adjacent interstitial chias- 
mata (//' = mXi r mXij- i), for example, //' = 2Xi 2 - 
2XU in 2Xi chiasmata, and Ii = 3Xh-3Xi 2 and 
3Xi 2 -3XU in 3Xi chiasmata. 

We denote the minimum value of Ic, Ii 
and It as Ic Mi „, Ii Mi „ and It Mi „. In the same 
manner, the maximum //' value on mXi arms 
is denoted as Ii Ma x(mXi), where Ii Max {mXi) = 
SL -{Ic Mi „ + It Mi „ + (m- 2)Ii Min ), m>2. For 
example, Ii M ax(2Xi) = SL — (Ic Min + It M m) and 
Ii M ax(3Xi) = SL - (Icum + It M m + Ii M in). We use 
Hmu.x = SL as a theoretically ideal case, where one 
interstitial chiasma (2Xi,) is located at the 
centromere and the other (2Xi 2 ) at the end of the 
arm, and thus Ic M m = It M m = 0. These values are 
useful for a quantitative description of chiasma 
distribution on the arms. 


There are three types of chiasma graph: (1) 
chiasma distribution graph; (2) chiasma fre- 
quency graph; and (3) chiasma interference 

(1) Chiasma distribution graph: this graph is 
useful for demonstrating the overall distribution 
pattern of chiasmata in a species examined, 
where the locations of the chiasmata on the arms 
are represented by two parameters; the size of the 
arms (SL) (ordinate), and the chiasma distance 
of Xi chiasmata (Xi) or Xt chiasmata (Xt) from 
the centromere (abscissa) [Fig. 2(a)]. 

The lXi, 2Xi u 2Xi 2 , and lXt chiasmata shown 
in Fig. 1(a) and 1(b) are plotted on the chiasma 
graph in Fig. 2, as examples. In the figure, each 
arm is shown temporarily by horizontal thin 
lines of relevant size, and the chiasma(ta) on the 
arms are represented by the symbols such as 
open circles for two interstitial chiasmata (2Xii 
and 2Xi 2 ), a solid circle for the lXi chiasma and 
short vertical bars for lXt chiasmata. To 
simplify the chiasma graph, the lines indicating 
the arms have been omitted from the practical 
chiasma graph. 

The basic concept of the chiasma "interference 
map" devised by Lawrie et al. (1995) is almost 

Location of chiasmata 
on standardized arms (SL') 

Location of chiasmata 
on arms (SL) % 

Fig. 2. Chiasma distribution graph (a) and chiasma 
frequency graph (b). In the chiasma distribution graph, 
locations of the chiasmata on the arms (SL) are defined by 
the distance from the centromere, and both the length of the 
arms (SL) and chiasma distance on the arms (Xc, Xi, Xt) 
are represented as percentages of the total autosomal length 
at diakinesis (Xc = 0, < Xi < SL, and Xt = SL). The 
locations of lXt, lXi, 2Xi,, 2Xi 2 and lXt chiasmata on the 
four arms shown in Fig. 1 are plotted on the distribution 
graph as examples. Locations of chiasmata on the 
frequency graph (Xc', Xi', Xt') are represented as the 
relative distance to the standardized arms (SL') with the 
length SL' =1, where Xc' = 0, < Xi' < 1, and Xt' = 1. 
For example, 2Xi, is plotted at the point 2Xi t from the 
centromere (c) in the distribution graph (a), but at 2Xi\ in 
the frequency graph (b), where 2Xi{ is estimated by 
2Xi{ = 2XU\SL. 

identical to our chiasma distribution graph. 
However, as they represented chiasma distri- 
butions of each chromosome separately, they 
could not analyse the overall distribution 
patterns of chiasmata quantitatively, which led 
to a fatal misunderstanding of the nature of 
terminal chiasma. 

(2) Chiasma frequency graph: the chiasma 
frequency graph [Fig. 2(b)] can be obtained by 
projecting the locations of the chiasmata (Xc, Xi, 



and Xt) on the chiasma distribution graph 
[Fig. 2(a)] to the standardized arms (SI/), where 
the length of SL' is 1.0 (SL' = 1.0). The cases of 
lXi, 2Xi, and 2Xi 2 chiasmata are shown in Fig. 
2(b) (see dotted and broken lines). The relative 
distance of Xc, Xi, and Xt chiasma on SL' 
(abbreviated Xc', XV, and Xt') is estimated as 
Xc' = Xc/SL = 0/SL = 0, < Xi' = Xi/SL < 1, 
and Xt' = Xt/SL = SL/SL = SL' = 1 .0. The 
number of' chiasmata is scored at every 0.1 

This graph is useful for demonstrating the 
gross frequency distribution of chiasmata on the 
standardized arms (SL'). This method can apply 
to the frequency distribution of chiasmata on 
arms with a specified length (e.g. SL = 8.0), 
which is basically identical to the conventional 
methods of Southern (1967) or Shaw & Knowles 
(1976) or Saadallah & Hulten (1983). 

(3) Chiasma interference graph: this graph is 
useful for demonstrating an overall distribution 
pattern of // values of mXi chiasmata on arms 
with various SL values, by which Ii Min and 
liMaximXi) values can be estimated statistically. 
Further details will be described later in Fig. 6. 




Chiasma distributions of a total of 600 
chromosome arms obtained from 50 cells at 
diakinesis are shown in Fig. 3 using the chiasma 
distribution graph [Fig. 3(a)] and the chiasma 
frequency graph [Fig. 3(b)]. The results are 
summarized as follows: 

(1) interstitial chiasmata (lXi, 2Xi and 3Xi) 
are distributed as a whole randomly and almost 
uniformly on the arms with the range of 
3.4 ^ SL ^ 15.2, except for the chiasma blank 
regions at the centromere and telomere, which 
are defined by Ic m „ and It Min [Fig. 3(a)]; 

(2) as more than 95% of Ic and // values are 
Ic ^ 0.8 and // ^ 0.8, we estimate Ic M m = 0.8 and 
It M m = 0.8. These values are constant in all arms 
with 3.4 ^ SL [dotted lines in Fig. 3(a)]. These 
results were reconfirmed by additional data from 
720 arms (60 cells) obtained from a different 

individual, those data are not shown in Fig. 3(a), 
but are included in Figs 3(b) and 4; 

(3) the uniform distribution of Xi chiasmata 
in Fig. 3(a) is represented quantitatively by a 
constant frequency of Xi chiasmata in the 
chiasma frequency graph [Fig. 3(b)], where 
9.36 + 1.37% in the range of 0.2 ^ Xi' ^ 0.9. 
The lc M m and It Min values are not clear in this 
graph, but it is noteworthy that the frequency of 
Xt chiasmata is remarkably higher (24.5%) than 
the mean frequency of Xi chiasmata; 

(4) the lXi fraction (lXi of lXi or lXi.IXt 
chiasmata) is distributed broadly between lc Min 
and It Min in the arms with 3.4 ^ SL ^ 12.4 [Fig. 
3(a), black solid circles and blue solid ovals with 
a bar]. On the other hand, the 2Xi fraction 
appears frequently in the large arms with 
6.4 ^ SL (especially in the range of 
8.0 ^ SL < 10.0), and shows a bipolar pattern 
(2Xi, is distributed proximally and 2Xi 2 distally) 
[Fig. 3(a), black open circles and blue open ovals 
with a bar]. As is demonstrated more clearly in 
the chiasma frequency graph, the lXi and 2Xi 
fractions are distributed in a mutually compensa- 
tory manner in the range of 0.1^ Xi' < 0.9 
[Fig. 4(b)]; 

(5) there is a tendency for the mXi of wXi.IXt 
chiasmata to be distributed more proximally 
[blue solid and open ovals with a bar in Figs 3(a) 
and 4(c)], of which the It value is 
SL — mXi,,, ^ 2.8 in all arms. We discuss in a 
later section that the minimum value [abbrevi- 
ated It M ,„(mXi.\Xt) = 2.8] is useful as an index 
for the Xt dissociation. 


We attempted to check the nature of the 
terminal chiasmata (Xt) by the PRINS technique 
with a synthesized oligonucleotide primer 
(CCCTAA) 7 to telomeres (TTAGGG) 7 . 

The results are summarized in Fig. 5. Mus 
platythrix has 26 acrocentric chromosomes 
(2m = 26). As clearly demonstrated in Fig. 5 
(arrows), four or two telomere signals are 
associated at the termini of bivalents identified as 
Xt chiasmata. In these cases, the telomere signals 
are consistently inside the lateral edges of 
bivalents, and they are detected as a constriction 


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or a narrow slit in bivalents stained by Giemsa. 
On the other hand, if there is an interstitial 
chiasma (Xi) in the subterminal regions, the 
paired telomere signals are located perpendicu- 
larly to the axis of the bivalents, or in other 
words, they project over the lateral edges of the 
bivalents (Fig. 5 arrowheads). These PRINS 
data indicate that most of the terminal chiasmata 
(Xt) we identified were either telomere- 
telomere associations or a special recombination 
which occurred within the telomeres or the 
subtelomeric regions. 


The // values of the 2Xi and 3Xi fractions are 
estimated as 2Xi 2 -2XU, 3Xi,-3Xi 2 and 3Xi 2 -3XU, 
which are represented by open circles or solid 
triangles in the chiasma interference graph 
(Fig. 6). In the figure, Ii Max is a theoretically 
ideal maximum value given by Ii Max = 2Xi 2 - 
2XU = SL, where 2Xi 2 = Xt = SL and 217, = 
Xc = 0. 

We found that there is a minimum // value 
(Ii M m), which is constantly 1.8% (Ii Mi „ = 1.8) in 
all arms in the range of 6.0 ^ SL ^ 14.5, and 
that the // values are distributed broadly 
between Ii Min and Ii Max (2Xi). The Ii Max (2Xi) 
values observed are almost consistent with 
those expected theoretically (Ii Max (2Xi) = 
SL-(Ic M ,„ + It mm) = SL-X.6) (Fig. 6, dotted line). 

In the 3Xi fraction, the Ii Max (3Xi) values 
were theoretically estimated as Ii Mia (3Xi) = 
SL-(Ic Mi „ + It Mi „ + Ii Min ) = 5L-(0.8 + 0.8 + 1.8) 
= SL-3A (Fig. 6, broken line), but the actually 
observed values [abbreviated // Ma v(3A7) oAj were 
lower than the expectation, which is 
/iW(3Ji)»*i = SL-5.6. The reason is not clear, 
but the small data size of 3Xi chiasmata available 
(only 32 cases) would be one of the reasons. 
Anyway, it is evident that the Ii Max (2Xi) and 
Ii M ax(3Xi)„ hs are parallel and Ii Max (2Xi) > 
Ii Mux (3Xi) 

These series of observations suggest that the 
// values of 2Xi and 3Xi fractions are 
mutually compensatory, and that they are 
distributed as a whole randomly and almost 
uniformly in the range of 1.8 ^ // ^ 5L-1.6, 
where SL > 6.0. 

(FXit AND FXi) 

We use two categories of chiasma frequency 
per cell (FXit and FXi). The FXit includes both 
interstitial (Xi) and terminal (Xt) chiasmata, but 
the FXi includes only Xi chiasmata. The 
conventional chiasma frequency corresponds to 
the FXit in our terminology. 

The FXit and FXi values observed in M. 
platythrix (n = 13) were FXit = 20.1 ± 2.0 and 
FXi = 14.6 +1.8 at diakinesis. The difference 
between them was significant, but not surpris- 
ingly large in this case (FXit-FXi = 5.5). 
However, it became remarkably larger in 
karyotypes with high chromosome numbers 
(n > 13). 

We examined the FXit and FXi values in 106 
animal species (51 mammals, three reptiles, five 
amphibians, 42 insects, four arthropods, and one 
echinoderm) with various chromosome numbers 
(n = 2-46) based on the meiotic chromosome 
figures which appeared in the references listed in 
Fig. 7. The results are summarized in Fig. 7(a) 
for FXi and Fig. 7(b) for FXit. In both cases, the 
FX values increased linearly with increase in the 
haploid chromosome number («), though the 
slope of FXit was steeper (the regression line is 
FXit = 1.2m + 3.1 and the correlation coefficient 
is 0.88) than that of FXi (FXi = OJn + 4.0 and 
c.c. = 0.85). 

We also found that the difference between 
FXit and FXi values (FXit-FXi) fluctuated 
remarkably in species with n > 10 (4 ^ FXit- 
FXi ^ 24). This phenomenon is closely related to 
the nature of terminal chiasma, which is 
discussed below. 



Evidence for telomere-telomere association 

As the chiasma terminalization hypothesis 
(Darlington, 1929, 1932) was negated by BrdU 
experiments (Tease, 1978; Kanda & Kato, 1980; 
Jones & Tease, 1984), the only remaining 
controversy relating to the Xt chiasma is the 
terminal chiasma in the literal meaning of the 
term or the achiasmatic terminal association. 



We emphasize that the nature of the Xt 
chiasma should be discussed based on the fine 
structure of chromosomes in which the SC ends 
at pachytene are attached to the nuclear 
membrane by the telomere and telomere-associ- 
ated proteins (Moens & Pearlman, 1990), a 
structure that has been known as the basal knob 
(Solari, 1970) or the terminal-attachment plaque 
(Moses, 1977). 

If the Xt chiasma is the recombination nodule 
(RN)-mediated recombination as well as the 
interstitial chiasma (Xi), the late recombination 
nodules (late-RNs) should appear at the basal 
knob. This expectation can be rejected, because 
late-RNs have never been observed on the basal 
knob of autosomal bivalents (e.g. Holm & 
Rasmussen, 1977; Zickler, 1977; Rasmussen & 
Holm, 1980; Lie & Laane, 1982; von Wettstein 
et al., 1984; Zickler et al., 1992). The 
pseudoautosomal region of the sex chromo- 
somes, the only exceptional case, is discussed in 
Appendix A. 

These negative observations were strength- 
ened recently based on immunofluorescence 
studies by Baker et al. (1996). They observed 
early and late pachytene spermatocytes of 
C57BL/6 mice with the Rad51 and Mlhl 
antibodies. The Rad51 can detect the 
synaptonemal complex (SC), and the Mlhl can 

identify the recombination nodule. So far, 
their figures have demonstrated that both ends 
of SCs are swollen in all bivalents at late 
pachytene, corresponding to the basal knob. 
We attempted to measure their length and 
obtained 0.74 + 0.21 of the total SC length of 
autosomal bivalents. In the figure, the signals of 
Mlhl appeared consistently outside the basal 
knob, and never at the strict SC ends. This 
indicates clearly that crossing-overs by means of 
RN-mediated recombinations are suppressed in 
the subterminal regions (0.74% from the 

As the size of the Mlhl suppressed 
regions (0.74) are almost the same as that of 
the chiasma blank regions It Mi „ = 0.8 [Fig. 3(a)], 
the discrimination of Xi chiasmata from 
Xt chiasmata would not be affected seriously 
by the accuracy of chiasma measurement or 
by the pseudo-terminalization of subterminal 
Xi chiasmata (Jones, 1978) (for details see 
Appendix B). 

The PRINS analysis of telomeres in this paper 
revealed that the termini of bivalents identified as 
terminal chiasma (Xt) are associated end-to-end 
by telomeres at diakinesis (arrows in Fig. 5). This 
result is consistent with the achiasmatic terminal 
association model in mice (Imai & Moriwaki, 
1982) and in grasshoppers having terminal 



50 - 

Haploid chromesome number (n) 

Fig. 7. Two categories of chiasma frequency per cell (FXi and FXit) in animals with various haploid chromosome numbers 
(2 ^ n ^ 46). (a) FXi values are estimated based only on Xi chiasmata (recommended in the present paper); (b) FXit values 
include both Xi and Xt chiasmata (corresponding to the conventional chiasma frequency). In both cases, FX values are 
proportional to the haploid chromosome number («). References cited. Mammals (#) (51 species): Ashley et al. (1989a, b); 
Book & Kjessler (1964); Breckon & Savage (1982); Brodin et al. (1995); Castro-Sierra & Wolf (1968); Chandley (1989); 
Dutrillaux & Rumpler (1977); Evans et al. (1964); Ford (1969); Gropp & Citoler (1969); Gropp et al. (1972); Hulten (1974); 
Hayata (1973); Hayman & Sharp (1981); Jagiello (1969); Matthey (1963); Meredith (1969); Ohno & Weiler (1961); Page 
(1973); Pearson et al. (1970); Pogosianz (1970); Polani (1972), Rodman & Biedler (1973), Rausch & Rausch (1974), Sasaki 
& Makino (1965), Sbalqueiro et al. (1984), Schmid et al. (1988), Sharma & Raman (1972), Therman & Susman (1993), 
Yonenaga (1972), Wahrman & Gourevitz (1973), Zimmerman (1974). Reptiles (A) (three species): King & Hayman (1978), 
Pennock et al. (1969), Wright (1973). Amphibians (■) (five species): Chandler et al. (1993), Green & Sharbel (1988), 
Guillemin (1967), Schmid (1980). Insects (O) (42 species): Antonio et al. (1993), Buss & Henderson (1988), Camacho et 
al. (1980), Cardoso et al. (1974), Dearn (1974a, b), Fiskesjo (1974), Fontana & Vickery (1973, 1976), Gibson & Hewitt 
(1972), Gosalvez et al. (1988), Hartman & Southern (1994), Henderson (1971), Henriques-Gil et al. (1982, 1983), Hewitt 
& John (1968, 1971), John (1973, 1990), John & Claridge (1974), John & Freeman (1974, 1975a, b), John & Henderson 
(1962), John & Hewitt (1965, 1966), John & King (1977, 1980, 1982, 1985b), John & Lewis (1965a, b), Keyl & Hagele (1971), 
Lewis & John (1959, 1966), Lucov & Nur (1973), Nance et al. (1990), Nankivell (1976), Nolte (1964), Nur (1969, 1981), 
Papeschi (1991), Rufas et al. (1986), Santos & Giraldez (1978), Schroeter & Hewitt (1974), Shaw (1970a, b, 1976), Shaw 
& Knowles (1976), Shaw & Wilkinson (1978), Shaw et al. (1976), Southern (1967), Suja et al. (1994), Tease & Jones (1978). 
Arthropods (□) (four species): Gorlov et al. (1995), Oliver et al. (1974), Pelliccia et al. (1991). Echinoderms (A) (one species): 
Smith- White (1968). 

heterochromatin segments (John & King, 
1985b), and also with the indisputably achias- 
matic X-Y chromosome associations found in 
various mammals (e.g. Solari & Ashley, 1977; 
Sharp, 1982; Joseph & Chandley, 1984; Wolf 
et al., 1988). 

Based on these series of arguments, our 
conclusion is that most conventional terminal 
chiasmata (Xt chiasmata) are either telomere- 
telomere associations or RN-independent re- 
combination in telomeres (Ashley, 1994), both of 
which occur inside the chiasma blank regions 
defined by It M m = 0.8. 

Dissociation of Xt chiasmata 

Imai & Moriwaki (1982) revealed that the 
dissociation of Xt chiasmata accelerates from 
diplotene to metaphase I in BALB/c mice via the 
contraction of bivalents, by which the conven- 
tional chiasma frequency per cell (FXit) de- 
creases at metaphase I (FXit = 25.4 ->■ 22.5). 
Contrary to FXit, the FXi value is constant 
through diakinesis and metaphase I 
(FXi = 17.0 + 1.0), because the bias due to 
the dissociation of Xt chiasma is excluded 
there. The dissociation of Xt chiasma 



during meiosis I was reconfirmed recently in the 
Chinese hamster (FXit = 19.3 + 1.8 -+ 17.5 + 
1.2, while FXi = 15.7 ± 1.2) (Wada & Imai, 

Baker et al. (1996) observed in C57BL/6 
mice that the number of Mlhl foci at early 
pachytene is 65 + 12 per cell and the number 
decreases gradually to stabilize at mid-pachytene 
(31+2 in females and 22+1.5 in males). 
The Mlhl foci at early and mid-pachytene 
correspond, respectively, to early-RNs and 
late-RNs. They did not refer to the number 
of Mlhl foci at late pachytene, but we suspect 
that the average number would decrease down 
to ca. 17 as can be seen in one of their 
figures. Note that the value 17 is comparable 
to FXi = 17 in BALB/c mice. This may not 
be coincidental, because the late-RNs at late 
pachytene correspond 1 : 1 to the chiasmata at 
diakinesis (for reviews see Carpenter, 1987; 
Ashley, 1994; Loidl, 1994; Moens, 1994; Egel, 
1995; Scherthan, 1997). 

We propose the following two lines of 
observations as additional supporting evidence 
for the dissociation model. 

(1) We demonstrated in M. platythrix that 
the mXi fractions are distributed proximally 
on the arms, and are characterized by 
It Min {mXi.\Xt) = 2.8 in the chiasma distribution 
graph [Fig. 3(a), blue solid and open ovals with 
a bar]. These data are interpretable consistently 
only assuming that the Xt of mXi.IXt chiasmata 
dissociates if the distance between the mXi,„ 
chiasmata and the termini of the bivalents is less 
than 2.8%, probably due to elasticity of the 

(2) The remarkable fluctuation of FXit-FXi 
values in animal species with n > 10 (4 ^ FXit- 
FXi ^ 24) can be attributed simply to species 
specificity in the dissociation of Xt chiasmata, 
because we can expect FXit = FXi if all Xt 
chiasmata dissociate, but FXit > FXi if the 
dissociation is incomplete. For the case of 
humans see Appendix C. 

We stress that the species specificity and 
cell-stage dependence of chiasma terminalization 
proposed by Darlington (1932) can be inter- 
preted more simply and consistently by the 
dissociation model. 


Assuming there is a causal relationship among 
interstitial chiasma (Xi chiasma), crossing-over, 
and RN-mediated recombination, and if the 
conventional terminal chiasma (Xt chiasma) can 
be replaced by the telomere association or the 
RN-independent recombination in telomeres, 
the chiasma would have at least three categories 
of functions: (1) cytological function for locking 
bivalents, (2) genetic function for shuffling genes; 
and (3) evolutionary function for promoting 
chromosome evolution. 

It is well known that at least one chiasma is 
necessary for "regular bivalent disjunction at 
anaphase I" (John, 1990). Both interstitial (Xi) 
and terminal (Xt) chiasmata are functional under 
this classical meaning. 

If we use, however, the chiasma in respect of 
gene shuffling, only the Xi chiasma is function- 
ally appropriate. Achiasmatic telomere associ- 
ation and RN-independent recombination in 
telomeres, both of which occur within the 
chiasma blank region (It Mi „), are not functionally 
effective for gene shuffling. This indicates that 
the conventional Xt chiasma should be excluded 
from the computation of chiasma frequency per 
cell (FX), because FX is the parameter of gene 

The evolutionary function of chiasma was first 
proposed in the minimum interaction theory by 
Imai et al. (1986, 1988). In that theory, 
chromosome interactions in pachytene nuclei 
through Xi chiasmata play the central roles in 
chromosome evolution. The genetic and evol- 
utionary functions of interstitial chiasma are 
discussed in more detail below. 


Distribution patterns of interstitial chiasmata 

We found from the chiasma graph analysis of 
M . platythrix that the overall distribution of wXi 
chiasmata is principally random and uniform 
except for the centromere region (Ic Mi „ = 0.8) 
and the telomere region (It Min = 0.8) [Fig. 3(a)]. 
On the other hand, the mXu, mXi 2 , . . ., mXi m 



chiasmata seem to be distributed non-randomly 
on the arms, and their distribution patterns are 
different in terms of the m values and the size of 
the arms (SL) (Fig. 8). 

In the small arms (3 < SL < 6), only lXi 
chiasmata appear and their distribution centers 
narrowly around XV = 0.5 [Fig. 8(b), solid line]. 
Such a monomodal distribution results partly 
from the heterogeneous arms involved and partly 
from the constancy of Ic Mi „ and lt M m values. Such 
a pattern has actually been observed in 
grasshoppers (Henderson, 1963; Southern, 1967) 
and humans (Hulten, 1974). 

In the medium-sized arms with 6 ^ SL < 10, 
lXi and 2Xi chiasmata appear, where the 
frequency distribution is monomodal in the 
former but bimodal in the latter [Figs 4(b) and 
8(c)]. Jones (1984) found long ago the same 
patterns in a grasshopper Chorthippus brunneus. 
We emphasize that these distributions compen- 
sate each other and the gross frequency of lXi 

and 2Xi chiasmata becomes constant [Fig. 8(c), 
dotted line]. 

In the large-sized arms with 10 ^ SL, lXi, 2Xi 
and 3Xi chiasmata overlap broadly [Fig. 8(a)], 
though their gross frequency distribution is again 
flat by compensating each other [Fig. 8(d), 
dotted line]. 

The same patterns have been observed in other 
mammalian species such as Chinese hamsters, 
BALB/c mice, domestic dogs (Wada & Imai, 
1995) and in parasite flukes Trematodes (Hirai 
et al., 1996a). Furthermore, these generalized 
distributions are consistent with the frequency 
distributions of late-RNs in humans (Rasmussen 
& Holm, 1984) and of genetic recombination 
in Drosophila melanogaster (Charles, 1938; 
Lindsley & Sandler, 1977). 

Chiasma interference distance (/) 

The interference distance (z) of Mather (1937) 
corresponds to the interstitial interference 

Fig. 8. Generalized distribution patterns of lXi (O), 2Xi (O), and 3Xi (O) chiasmata in the chiasma distribution graph 
(a) and in the chiasma frequency graphs (b, c, d). For terminologies see Figs 1 and 2. lXi (#); 2Xi (O); 3Xi (A)- 



Table 1 

It M in and Ii M in values in mammals and trematodes 


number (n) 





Chinese hamster 





Wada & Imai, 1995 

Mus platythrix 





Present paper 

BALB/c mouse 





Wada & Imai, 1995 

Domestic dog 





Wada & Imai, 1995 


Schistosoma mansoni 





Hirai et al., 1996a, b 

Paragonimus ohirai 





Hirai et al., 1996a, b 

distance (//') in our terminology (Fig. 1). 
However, contrary to Mather's expectation, the 
//' value alters at random between Ii Min and 
Ii Ma x(mXi) (Fig. 6), and the Ii Min value is constant 
(Ii Mi „ = 1.8) in all arms of all species observed 
(Table 1). 

These results are consistent with the polym- 
erization model for chiasma formation (King & 
Mortimer, 1990), in which RNs attached to the 
SC initiate the polymerization reaction and the 
growing polymers along the central element 
reject other RNs. In this model, Ii Mi „ = 1 .8 means 
the minimum distance covered by polymers. The 
effect of polymerization in rejecting other RNs 
seems to decrease gradually in the areas 
1.8 < // s$ Ii Max (mXi) (Fig. 6). 

The centromeric interference distance (Ic) is 
synonymous with the differential distance (d) of 
Mather (1937). He assumed that the d value is 
correlated with the arm length, but our results 
indicated that the Ic M m value is species-specific 
(Ic Min = 0.5-1.0) (Table 1), but constant in all 
arms of the same species. The Ic Min results from 
the well-known fact that chiasma formation is 
inhibited in centromeric heterochromatin (John 
& Miklos, 1979; Lake, 1986). 

Mather postulated in the same paper that 
small chromosomes less than d (small "arms" in 
our terminology) have one obligate chiasma 
(Xt), and that in large chromosomes longer than 
d, the number of chiasma per chromosome 
(FXit/SL) is proportional to the chromosome 
length, because chiasmata appear at a constant 
interval defined by i. 

We propose a more simple model in which the 
frequency of Xi chiasmata per arm (FXi/SL) is 
proportional to the arm length (Fig. 9), because 

the gross frequency distribution of mXi chias- 
mata is uniform along the arms except for Ic Mi „ 
and It Mi „ (Figs 3 and 8). In our model, the 
frequency of Xi chiasmata per arm becomes less 
than one (FXi/SL < 1) in small arms with 
SL ^ 6-7 (Fig. 9). This does not prevent normal 
disjunction at anaphase I, because their termini 
are connected by telomeres [thick vertical bars in 
Fig. 3(a), and arrows in Fig. 5]. 

A preliminary study of genetic recombination 
using DNA markers has shown that the 
frequency of genetic recombinations per 
chromosome is linearly proportional to the 
length of chromosomes in B6-3MSM male mice, 
which is highly consistent with the FXi/SL values 
of BALB/c in Fig. 9 (Shiroishi, pers. commun.). 

2 4 6 8 10 12 14 16 

Size of arm (SL) % 

Fig. 9. Correlation between the frequency of Xi 
chiasmata per arm (FXi/SL) and size of the arms (SL) in 

Mus platythrix ( #), Chinese hamster ( O) and 

BALB/c (—A) mouse. The FXi/SL values are linearly 
proportional to the size of the arms (SL). Note that the 
values are lower than 1 .0 in small arms with SL < 6-7. This 
would not induce any irregular disjunction at anaphase I, 
because the bivalents are locked by the achiasmatic 
telomere association. 




We revealed that the FXi values of 106 animal 
species were approximately linearly proportional 
to the haploid chromosome number («). The 
regression line which was obtained by the least 
squares method is FXi = OJn + 4.0 [Fig. 7(a)], 
where the correlation coefficient is 0.85. This 
unexpected result can be explained reasonably, if 
it is assumed that the total SC length was 
constant in the animals examined. A brief outline 

It may be safe to assume that the bivalent 
length at diakinesis is proportional to the SC 
length at pachytene, because the SC is formed 
along the total length of the bivalent at 
pachytene (Rasmussen & Holm, 1980). On the 
other hand, there are some fragmentary data 
that in animals such as Drosophila melanogaster , 
Bombix mori, Cricetulus griseus and Homo 
sapiens, the SC length is fairly constant 
(110-231 um; Lie & Laane, 1982) in spite of 
remarkable differences in their genome size 
(0.18-3.5 pg; Cavalier-Smith, 1985). 

The difference in genome size may be buffered 
by increasing the chromatin packing ratios. For 
example, the SC length can be conserved 
theoretically, if the width of the half bivalents is 
larger in species with a large genome size than in 
those with a small genome size, a fact that is 
known empirically by cytologists. 

Our chiasma graph analysis provides substan- 
tial bases for the minimum interaction theory 
(Imai et al., 1986), because the chromosome 
evolution of eukaryotes is described in the 
theory based on chromosomal interactions 
under the hammock structure in pachytene 
nuclei, where the crossing-over in a broad 
sense (including both RN -mediated and RN- 
independent recombinations) and miss-resol- 
ution of interlocking are assumed to be the prime 

In the minimum interaction theory, chromo- 
somes evolve as a whole toward an increase in 
chromosome number. The biological significance 
of an increase in chromosome number is 
considered to be evolution-adaptive for minimiz- 
ing the genetic risk due to deleterious chromo- 
some mutations, such as reciprocal transloca- 

tion. This theory was supported recently at the 
molecular level by the finding of genomic 
dispersion of 28S rDNA in the ant genus 
Myrmecia (Hirai et al, 1994, 1996b; Meyne et 
al, 1995). 

Our present finding of a positive correlation 
between the chiasma frequency per cell (FXi) 
and the haploid chromosome number («) [Fig. 
7(a)], seems also to be evolution-adaptive, 
because gene shuffling can be expected to be 
accelerated in species with a high chromosome 
number. Therefore, we propose this as another 
mechanism of biological significance for increas- 
ing the chromosome number during the course 
of eukaryotic chromosome evolution. 

This study was supported in part by a Grant-in-Aid 
of The Ministory of Education, Science, Sports and 
Culture of Japan (08454279). 


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RN-mediated Rearrangement in the 
Pseudoautosomal Region and RN-independent 
Recombination in Telomeres or Subtelomeric 

According to Solari (1994), the end-to-end 
association in the pseudoautosomal region 
(PAR) of the human and mouse sex chromo- 
somes is RN-mediated recombination. However, 
Baker et al. (1996) revealed more recently that 
the Mlhl foci at PAR were detected at early 
pachytene, but not at late pachytene in C57BL/6 
mice, thereby suggesting the alternative possibil- 
ities that the RNs observed at PAR might be 
early-RNs but not late-RNs, or that if they are 
late-RNs, they would appear less frequently. 

The X-Y dissociation found in inter-subspe- 
cies hybrids between BALB/c and Mus musculus 
molossinus also suggests an achiasmatic terminal 
association (Imai et al., 1981; Matsuda et al., 
1982, 1983), of which the genetic factor "Sxa" 
controlling the end-to-end association of the sex 
chromosomes in mice was found near the distal 
end of the X chromosome (Imai et al., 1990). 

These alternative observations can be inter- 
preted consistently by a "double-lock" mechan- 
ism (Wada & Imai, 1995), in which the X and Y 
chromosomes are assumed to be locked either by 
an achiasmatic telomere-telomere association or 
by the RN-mediated recombination at PAR. 

If we adopt the latter interpretation of 
RN-mediated recombination at PAR, such 
recombinations are restricted to the narrow 
regions (2.6 or 0.4 Mbp from the short or long 
arm telomere end) in human pseudoautosomal 
regions. Six genes (MIC2, XE7, ASMT, ANT3, 
IL3RA, CSF2RA) were identified in the former, 
but none in the latter (Rappold, 1993). In the 
case of mice, only the Sts gene is known (Keitges 
et al., 1985). These molecular data suggest that 
the obligate chiasma at PAR (even if it occurs) 

would have significantly less effect on gene 

In connection with this, several STIR elements 
(sub/elomeric interspersed repeats obtained 
from PAR) were detected recently in the 
subtelomeric regions of human autosomal 
chromosomes (Rouyer et al., 1990). They 
revealed that recombinations occur frequently in 
STIRs, and suggested telomere-telomere inter- 
actions, which could play a role in promoting the 
initiation of pairing at meiosis. These recombina- 
tions fall under the category of RN-independent 
recombination proposed by Ashley (1994), which 
is an event occurring in the chiasma blank region 
(It M m) in our terminology. 


Minimum Terminal Interference Distance (/*«,„) 
and the Accuracy of Measurement of Chiasma 

The accuracy of chiasma measurement de- 
pends mostly on the width of the half bivalents, 
which is ca. 2/3 of the width of the half bivalents 
at diakinesis, and their percentage to the total 
autosomal length is 0.5-0.6 in Chinese hamsters, 
BALB/c mice (Wada & Imai, 1995) and M. 
platythrix. Note that the values are almost 
comparable to the It Mi „ values (It Min = 0.5-0.8) 
(Table 1). 

These data suggest that some mXi m chiasmata 
located in the subterminal region {It < 0.8) may 
be misidentified as Xt chiasmata, known as the 
pseudo-terminalization of subterminal Xi chias- 
mata (Jones, 1978). This possibility can be 
rejected by the immunofluorescence data show- 
ing that the RN-mediated recombinations 
occurring by means of Mlhl do not appear in the 
subterminal regions 0.74% from the SC ends 
(Baker et al., 1996). In other words, the 
RN-mediated recombinations can be identified 
accurately as Xi chiasmata by our measurement 

The pseudo-terminalization observed in rye 
(Secale cereale) by Jones (1978) is a special case 
that occurred in chomosomes having large 
heterochromatin blocks at the distal ends. This 
is an inappropriate example for chiasma graph 
analysis, and does not mean that Xt chiasmata 



of other eukaryotes always result from the 
pseudo-terminalization of subterminal Xi 


Chiasma Frequency per Cell in Humans 

The chiasma frequency of humans estimated 
by Hulten (1974) was 50.61 + 3.87. We reexam- 
ined both the FXit and FXi values based on the 
12 meiotic figures that appeared in the literature 
by Book & Kjessler (1964), Evans et al. (1964), 
Sasaki & Makino (1965), Ford (1969), 
Meredith (1969), Pearson et al. (1970), Page 
(1973), Hulten (1974) and Therman & Susman 
(1993). Our results were FXit = 51.08 + 4.11 and 
FXi = 30.83 ± 3.87. 

In spite of the small sampling size, the FXit 
value of our estimation is almost exactly the 
same as that by Hulten. On the other hand, 
the FXi value is markedly lower than the FXit 
value (FXit-FXi = 20.25). These data indicate 
that the chiasma frequency determined by 
Hulten corresponds to the FXit in our terminol- 
ogy and thus both Xi and Xt chiasmata are 

The extremely high FXit value of humans may 
be interpreted simply by assuming that the 
telomeres of humans tend to associate rather 
tightly. However, the chiasma frequency deter- 
mined by Fang & Jagiello (1988) (45.33 ± 4.52) is 
obviously due to misidentification of artificial 
crossovers in twisted bivalents at early/mid